Which of the following numbers is a factor of 88? ${5,7,11,12,14}$
Answer: By definition, a factor of a number will divide evenly into that number. We can start by dividing $88$ by each of our answer choices. $88 \div 5 = 17\text{ R }3$ $88 \div 7 = 12\text{ R }4$ $88 \div 11 = 8$ $88 \div 12 = 7\text{ R }4$ $88 \div 14 = 6\text{ R }4$ The only answer choice that divides into $88$ with no remainder is $11$ $ 8$ $11$ $88$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $11$ are contained within the prime factors of $88$ $88 = 2\times2\times2\times11 11 = 11$ Therefore the only factor of $88$ out of our choices is $11$. We can say that $88$ is divisible by $11$.